Graphics Reference
In-Depth Information
Commutative Diagram.
In general, if one has a directed graph where the nodes are
sets and the arrows correspond to maps between these sets, then this is said to con-
stitute a commutative diagram if, whenever two directed paths start and end at the
same points, the corresponding composition of maps is equal. Commutative diagrams
are nice to have and the terminology is useful in many areas of mathematics. As an
example, consider the diagram
f
A
ææ
B
g
Ø
Ø
F
C
ææ
D
G
If G(g(a)) = F(f(a)) for all a ΠA , then the diagram is said to be
commutative
.
